In the first part of the talk, I will present a recent approach to black holethermodynamics where the Bekenstein-Hawking entropy is regarded asa nonextensive Tsallis entropy, and the thermodynamic and stabilityproperties of the system are obtained via its formal logarithm, theRényi entropy function. In the second part, I will introduce a parametricmodel for cosmic information entropy in order to consider the problemof information entanglement between spatially separated but causallyconnected regions of the universe.

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